Improvement of Industrial Maintenance Plans through Assistance-Driven Reliability-Centered Maintenance and Case-Based Reasoning Design

: The present work builds on studies where the industrial market is currently characterized by a highly variable demand in terms of the quantities and flexibility of manufacturing or mass customization, which translates into a more demanding production context in terms of the continuous changes that are required in the production systems, the effect of which results in an increase in the fatigue of the machines that make up the production systems. However, current production systems tend to use highly communicative and sensorized cyber–physical systems; these characteristics can be used to integrate them into decision-assisted systems to improve the availability of the industrial plant. The developed assisted system focuses on collecting and taking advantage of historical knowledge of industrial plant failures and breakdowns. By ideally integrating the reliability-centered maintenance (RCM) methodology and case-based reasoning (CBR) algorithms implemented in a Java application, it is possible to design maintenance plans that are adjusted to the real and changing operational context of any industrial plant. As a result, faster and more accurate decisions are made, because they are based on data. This article focuses on improving certain aspects of the developed assisted system by adding more value by incorporating fuzzy logic (FL) techniques. The aim is to improve the way of entering information about risk factors and their relative importance by incorporating natural language instead of a numerical score, resulting in increased precision in the calculation of the risk priority number (RPN) of the new cases that are incorporated into the assisted system. On the other hand, an attempt has been made to correct two of the main inherent and recognized weaknesses in the classic RPN calculation method by implementing an appropriate mix of fuzzy logic techniques.


Introduction
Decision-making systems continue to be used in the analysis of maintenance activities and, in particular, in the risk assessment of their tasks.Planning maintenance tasks can detect failures in advance and avoid production stops, and this objective has been considered in the development of strategic, tactical, and operational systems due to their influence on long-, medium-, and short-term decisions.At a strategic level, Al-Turki [1] concludes that planning should ensure alignment with other areas of the organization and the definition of a structured plan; along this line of reasoning, systems that integrate strategic functions with a Balanced Score Card (BSC), using the Analytic Hierarchy Process, allow the Key Performance Indicators (KPIs) to be associated with the goals of the company [2].At the tactical level, models that are based on BSC, capable of discovering structures and behavior patterns that are relatively hidden in work orders, and use machine learning have been analyzed [3].Regarding the operational level, a computer application has been designed, implemented, and validated through the incorporation of reliability-centered maintenance (RCM) cases that were successfully carried out on equipment [4] or on a productive process [5].
Thus, proposals that integrate maintenance plans that are oriented toward reliability, risk, and cost have been defined [6].In circumstances where there are no training data, tools for general mechanical functional modeling have been developed [7].Particular cases, such as multistage industrial machines, have been analyzed, concluding that for a preventive maintenance strategy, the study of individual maintenance times allows for defining the KPIs [8], while a predictive maintenance strategy should be used when an unexpected failure occurs [9].Song et al. [10] established a framework based on RCM that allows for automatic evaluation of the consequences of all equipment failures that are predefined, considering data from multilevel flow modeling.
The application of methodologies such as RCM and Failure Modes, Effects, and Criticality Analysis (FMECA) allows us to know the risk priority number (RPN); this number is a combination of the probability of severity, occurrence, and detectability of risks.This indicator has been used to validate decision-making models with different scales.For example, refs.[11,12] proposed a calculation for FMECA based on four fuzzy logic systems.
In parallel, works on the relationship between maintenance and industry 4.0 have been developed, exploring the possibilities of integrating digitalization tools [13], of integrating predictive techniques based on data projection with autonomous learning tools [14,15], and improvement of an assisted system that is integrated into AR (Augmented Reality) or MR (Mixed Reality) management environments [16]; the latter case is analyzed as support to intelligent on-site operators and external technicians from CPS (Cyber-Physical System) machine manufacturers.
As has been seen, there are numerous proposals in the field of maintenance planning, some innovative and others with improvements in existing systems.
This article aims to provide an assisted system with a more consistent calculation of the RPN, considering the way in which the defining risk factors are introduced.The intention is to address two shortcomings that are present in the classic method: the numerical scoring of risk factors by experts does not necessitate a language that is closer to human understanding and the assumption that risk factors are treated with the same importance for all proposed failure modes.From this point, this article attempts to analyze alternative methods to the classic RPN calculation and select those that more efficiently resolve both shortcomings.
The fuzzy logic methodology was chosen because of its proven success in using natural language.In addition, various studies have used fuzzy logic in Failure Modes, Effects, and Criticality Analysis (FMECA), including the calculation of RPN, with real case studies conducted in industrial production environments, as evidenced by studies employing the fuzzy FMECA approach compiled by Kabir and Papadopoulos [17].
Once suitable methods are identified, efforts will be made to incorporate them into the assisted system through implementation in its source code.The final objective of this study is to validate the newly proposed RPN method and subsequently address specific cases using the new score, derived from the refined RPN calculation.
The present work is structured in several sections.Section 2 shows the fuzzy logic methodologies that are employed and how they are integrated to establish the formulation of the new RPN calculation method.Section 3 shows how the new method has been implemented in the previously developed computer application, and a case study is presented to demonstrate the applicability of the proposed method on a real case, solved by the previously assisted system, so that it can be compared with both classic and enhanced RPN calculation methods.Subsequently, Section 4 discusses the results that were achieved with the improvement of the new proposed calculation method of RPN.Finally, in Section 5, the conclusions are collected in terms of novelty, results, and differences obtained between the RPN values according to the classic and proposed methods.

Fundamentals
The antecedent scholarly contribution articulated by Rodríguez-Padial et al. [5] was centered around a systematic approach for decision making regarding the formulation of customized maintenance plans within the precincts of a production plant.The overarching objective of this investigation was to provide an expert system that is designed to facilitate decision making in the crafting of maintenance plans, meticulously tailored to the authentic productive milieu of an industrial plant.This imperative customization was predicated on the harmonization of the company's strategic objectives in terms of tactical and maintenance operations [5].In essence, the aim of this study is to address a reliability conundrum by employing the established methodology of reliability-centered maintenance (RCM), underpinned by case-based reasoning algorithms (CBR).This strategic combination aspires to furnish an optimized maintenance solution that is adept at accommodating emergent challenges, as exemplified by novel cases.The primary intent of this endeavor was to systematically guide experts in the judicious application of the RCM method within the tangible operational framework of a plant.Consequently, the outlined methodology engenders three discernible advantages: the mitigation of human error, the assurance of a commendable level of excellence, and a pronounced reduction in the temporal commitment of the expert, which is consistent with the findings posited by Rahman et al. [18].To realize these objectives, a bespoke software application was engineered, poised to automatically undertake recovery, analysis, and adaptation when confronted with a nascent reliability issue.A pivotal advantage emanates from the abundance of historical cases, where the expert selectively considers the most analogous k-cases, adopting the k-nearest neighbors (kNN).This methodology proposes the three most comparable cases (k = 3) to the novel scenario, thereby enhancing the decision making process [5].The combination of the RCM method with the CBR methodology augments the expert's efficacy in RCM, which translates into substantial temporal savings, particularly in the intricate phase encompassing Failure Modes, Effects, and Criticalities Analysis (FMECA).
This seamless integration of both methodologies, implemented using the Java programing language, culminates in the development of an independent computerized RCM application that can be applied to diverse industrial environments [5].The conceptualization of the used RCM application unfolded in two pivotal stages.The initial phase witnessed the implementation of Failure Modes, Effects, and Criticalities Analysis (FMECA) through the CBR method, employing the jCOLIBRI environment, as depicted in Figure 1 by Recio-García et al. [19,20].Subsequently, in the second stage, the maintenance policy was articulated in accordance with a decisional flow chart that was tailored to the operational intricacies of the newly posed case.Consequently, the maintenance policy initially adopted for the recovered case was rendered obsolete.This nuanced adjustment stemmed from the acknowledgment that the maintenance policy is more contingent on the operational context in which the equipment is situated, emphasizing its effects rather than the failure mode, which is intricately associated with the equipment type and maintenance policies that are embedded within the productive context.
The first stage involves the application of the CBR flow to the FMECA segment of the RCM method, entailing the retrieval of failure modes within the case base.This involves a comparative analysis of the new problem, posed through queries.The second stage, encapsulated within the conductive RCM decision flow diagram within the CBR cycle's review activity, endeavors to reapply maintenance actions.This entails a comprehensive re-evaluation of parameters, including the risk priority number (RPN), maintenance task instruction, maintenance class, interval, and assigned workshop responsibility.The first stage involves the application of the CBR flow to the FMECA segment of the RCM method, entailing the retrieval of failure modes within the case base.This involves a comparative analysis of the new problem, posed through queries.The second stage, encapsulated within the conductive RCM decision flow diagram within the CBR cycle's review activity, endeavors to reapply maintenance actions.This entails a comprehensive reevaluation of parameters, including the risk priority number (RPN), maintenance task instruction, maintenance class, interval, and assigned workshop responsibility.
The essence of this study lies in the refinement of the second-stage method, namely, conductive RCM, focusing exclusively on the calculation of the risk priority number (RPN).This refinement entails an improvement in its approximation through an alternative evaluation methodology, specifically through the adjustment and weighting of the constituent risk factors.The attributes that are subjected to scrutiny in the second stage encompass the risk priority number (RPN), considering its occurrence, severity, and detection risk factors, along with the Proposed Task (PT), Initial Interval (II), Responsibility (R), and the novel maintenance policy or maintenance classification (MC).The application of the new maintenance policy adheres to the RCM decision diagram, systematically guiding the user through a series of questions to determine the applicable maintenance action within the given context.The culmination of the CBR cycle manifests in the retained activity, where the newly reviewed case is stored in the case base, constituting an additional instance in the RCM database case files.Our previous work demonstrated the application's efficacy in resolving a novel failure case during the first stage (CBR-RCM).In this initial phase, the input information for the new problem was entered into the query window, as shown in Figure 2. The problem was described as a functional failure, specifically "Do not center the axes", occurring within the Section labeled "EW", which in the installation was designated as "RESMAS" and on the Equipment labeled "AXIS".The application adeptly retrieved three analogous cases to the presented problem, presented in descending order of similarity in Figure 2. The user is afforded the autonomy to select the most suitable case from the three options, with the added capability of exploring other variables such as failure modes or effects that contribute to the FMECA.The essence of this study lies in the refinement of the second-stage method, namely, conductive RCM, focusing exclusively on the calculation of the risk priority number (RPN).This refinement entails an improvement in its approximation through an alternative evaluation methodology, specifically through the adjustment and weighting of the constituent risk factors.The attributes that are subjected to scrutiny in the second stage encompass the risk priority number (RPN), considering its occurrence, severity, and detection risk factors, along with the Proposed Task (PT), Initial Interval (II), Responsibility (R), and the novel maintenance policy or maintenance classification (MC).The application of the new maintenance policy adheres to the RCM decision diagram, systematically guiding the user through a series of questions to determine the applicable maintenance action within the given context.The culmination of the CBR cycle manifests in the retained activity, where the newly reviewed case is stored in the case base, constituting an additional instance in the RCM database case files.Our previous work demonstrated the application's efficacy in resolving a novel failure case during the first stage (CBR-RCM).In this initial phase, the input information for the new problem was entered into the query window, as shown in Figure 2. The problem was described as a functional failure, specifically "Do not center the axes", occurring within the Section labeled "EW", which in the installation was designated as "RESMAS" and on the Equipment labeled "AXIS".The application adeptly retrieved three analogous cases to the presented problem, presented in descending order of similarity in Figure 2. The user is afforded the autonomy to select the most suitable case from the three options, with the added capability of exploring other variables such as failure modes or effects that contribute to the FMECA.The second stage of the employed RCM process comprehensively reviews the contextual information of the new problem, as illustrated in Figure 3.With the user-entered data, encompassing the occurrence (O), severity (S), and detection (D), the new risk priority number (RPN) is automatically calculated, mirroring the classic method RPN = OxSxD.Conclusively, the redefined maintenance class clearly aligns with the RCM diagram.This signifies that users have been systematically guided through the questions in the diagram, and the newly revised case is then appended as the latest entry in the case base.This sequential refinement of the conductive RCM methodology accentuates the precision of RPN calculations, contributing to the overall robustness and efficacy of the maintenance planning process.

Improved RPN Methodology
In the design of this assisted system, the RCM methodology was integrated into a CBR cycle, resulting in a conductive RCM method, directing or conducting the RCM methodology in order to assist an expert efficiently from the beginning to the end, through all intermediate stages.During an RCM process, specifically within the FMECA analysis, each failure mode that is analyzed is classified by risk and evaluated by the risk priority number (RPN) to be subsequently prioritized.Although the classic RPN calculation method was implemented in the original design of the assisted system, it has certain disadvantages that will be discussed later.This work attempts to correct these deficiencies by implementing fuzzy logic (FL) techniques in the source code of the assisted system to make up for the aforementioned deficiencies with the current method.The following subsections briefly describe fuzzy logic and its use for calculating RPN, hereinafter referred to as fuzzy RPN or fRPN.

Fuzzy Logic
Fuzzy logic was developed by Zadeh [21] to deal with imprecise information expressed in human language.The fuzzy process involves transforming a set of numerical variables into a fuzzy set of values.A fuzzy set, A, in the discourse universe, U, is characterized by a membership function μA(x), where the membership function μA(x), which assigns a degree of membership of an element x to the fuzzy set A, ranges between 0 and 1.The fuzzy set A is mathematically defined according to Equation (1): A special case of fuzzy sets is fuzzy numbers, where they are characterized by being represented by an interval of real numbers and are usually denoted by these.(a, b, c), a,b,c ϵ ℝ, for the case of triangular fuzzy numbers, like those used in this work, and their membership function is as follows: The second stage of the employed RCM process comprehensively reviews the contextual information of the new problem, as illustrated in Figure 3.With the user-entered data, encompassing the occurrence (O), severity (S), and detection (D), the new risk priority number (RPN) is automatically calculated, mirroring the classic method RPN = OxSxD.Conclusively, the redefined maintenance class clearly aligns with the RCM diagram.This signifies that users have been systematically guided through the questions in the diagram, and the newly revised case is then appended as the latest entry in the case base.This sequential refinement of the conductive RCM methodology accentuates the precision of RPN calculations, contributing to the overall robustness and efficacy of the maintenance planning process.presented problem, the review process proceeds.The start of the second stage of the employed RCM process ensues promptly, entailing a comprehensive review of the contextual information on the new problem.In this iteration, incorporating the novel RPN calculation method, the risk factors that are associated with occurrence, severity, and detection are systematically considered.The new risk priority number (RPN) is automatically computed using linguistic terms through fuzzy logic.
It is noteworthy that, in contrast to the preceding RPN calculation method, the information entered is no longer numerical on a scale of 1 to 10, but rather comprises linguistic expressions such as low, medium, and high.As depicted in the initial three pop-up windows within Figure 3, new dialog boxes emerge, soliciting information on the relative importance of each risk factor, facilitated through a drop-down list of terms.This innovation represents a departure from the previous calculation methodology, in which such evaluations were not undertaken.In Figure 4, data on the values of the three risk factors of occurrence, severity, and detection are entered by choosing from a drop-down list the most appropriate term that defines each of them for the functional failure analyzed.In this way, the expert goes from trying to evaluate precisely and numerically to using a more natural language with human tolerance.As a result of the calculation, an information box appears with the new RPN value, calculated with the new implemented methodology, as shown in the last figure in Figure 4.
It should be noted that previously, the new method was validated with extreme and average values for the weights and risk factors, verifying RPN results in accordance with them.Finally, using similar input data for both classic/fuzzy weighted methodologies, RPN values are obtained, 300 vs. 336, respectively, resulting in a discrepancy of 1.78%, which indicates that the method has been well adjusted. (a)

Improved RPN Methodology
In the design of this assisted system, the RCM methodology was integrated into a CBR cycle, resulting in a conductive RCM method, directing or conducting the RCM methodology in order to assist an expert efficiently from the beginning to the end, through all intermediate stages.During an RCM process, specifically within the FMECA analysis, each failure mode that is analyzed is classified by risk and evaluated by the risk priority number (RPN) to be subsequently prioritized.Although the classic RPN calculation method was implemented in the original design of the assisted system, it has certain disadvantages that will be discussed later.This work attempts to correct these deficiencies by implementing fuzzy logic (FL) techniques in the source code of the assisted system to make up for the aforementioned deficiencies with the current method.The following subsections briefly describe fuzzy logic and its use for calculating RPN, hereinafter referred to as fuzzy RPN or fRPN.

Fuzzy Logic
Fuzzy logic was developed by Zadeh [21] to deal with imprecise information expressed in human language.The fuzzy process involves transforming a set of numerical variables into a fuzzy set of values.A fuzzy set, A, in the discourse universe, U, is characterized by a membership function µ A (x), where the membership function µ A (x), which assigns a degree of membership of an element x to the fuzzy set A, ranges between 0 and 1.The fuzzy set A is mathematically defined according to Equation (1): A special case of fuzzy sets is fuzzy numbers, where they are characterized by being represented by an interval of real numbers and are usually denoted by these.(a, b, c), a,b,c ϵ R, for the case of triangular fuzzy numbers, like those used in this work, and their membership function is as follows: The inverse operation, which makes it possible to convert a fuzzy number, A, into a real number, x, is called the defuzzification process, x(A), and there are various methods to calculate it, the most used being the centroid: Due to its simplicity and proven usefulness, the method of converting linguistic variables to fuzzy numbers used will be the L-R fuzzy method used by Baghbani et al. [22].The total score of a fuzzy number is as follows: where

Fuzzy Logic Applied in the Calculation of RPN (Fuzzy RPN)
The classic calculation of the risk priority number is obtained by Equation ( 7): where O, S, and D are, respectively, the risk factors that represent the probabilities of occurrence, severity, and detection of each failure mode evaluated.Each risk factor is evaluated within a numerical range of 1 to 10, so the RPN value is limited within a range of 0 to 1000.As mentioned above, the classic RPN calculation, although it is a widely used method, presents certain weaknesses, and its calculation method has been questioned in some application environments, as cited by Ben-Daya and Raouf [23], Bowles [24], Braglia et al. [25], Chang et al. [26], Gilchrist [27], Pillay and Wang [28], and Sankar and Prabhu [29].The disadvantages of this calculation are that although several authors list several, all agree on two.On the one hand, risk factors are evaluated numerically, from 0 to 10, by experts; therefore, natural language is not used, such as the use of linguistic variables that include values such as "low", "medium", or "high", which are more comfortable or close expressions for the human evaluator.On the other hand, as shown in Equation ( 7), the classic method of calculating RPN presents the same relative importance for the three risk factors O, S, and D. This is not always the case, depending on the criticality of each operational context; therefore, the relative importance of each factor must be weighted.To correct these weaknesses, fuzzy logic is used to calculate the risk priority number (RPN) through the three risk factors O, S, and D.
The methodology used by Baghbani et al. [22] tries to integrate expert judgment through fuzzy triangular membership functions that are associated with each risk factor, instead of the "crisp" numerical values of the classic method.Tables 1-3 show the linguistic variables that are used to evaluate the risk factors occurrence (O), severity (S), and detection (D) and their respective fuzzy numbers fNO, fNS, and fND.In the following columns, the values of the parameters are obtained as α y β and left µ L (A), right µ R (A), and total score µ T (A), using the L-R defuzzification method used by Baghbani et al. [22], according to Equations ( 4)-( 6) for each of the three risk factors, as defuzzified triangular fuzzy numbers, resulting in µ O as µ T (O), µ S as µ T (S), and µ D as µ T (D); these numerical values can be seen in the last columns of Tables 1-3, respectively, for each linguistic term.The classic RPN calculation method assigns the same relative importance to each risk factor.Although many authors decide to use fuzzy IF-THEN rules, such as Renjith et al. [30], building the rule base becomes very tedious due to the huge number of judgments issued by experts, which results in a lot of devoted time, even when rule reduction methods have been applied, as proposed by Cao et al. [31].Francis and Colli [32] tried to weight the severity risk factors, but despite their attempt, only one of the three risk factors was preweighted, so it was not considered a complete solution.Wang et al. [33] aimed to correct this effect without using fuzzy rules, avoiding asking the experts too much, and proposed to calculate RPN using fuzzy logic and fuzzy weighted geometric mean, thus avoiding the weakness that fairness entails in the relative importance of risk factors in the classic calculation of RPN calculation.The relative importance of each risk factor is considered a weight factor, W, and evaluated in linguistic terms using a triangular fuzzy function, whose fuzzy numbers are shown in Table 4.

Weights (W) fNW
Very High (0.75, 1, 1) High (0.5, 0.75, 1) Medium (0.25, 0.5, 0.75) Low (0, 0.25, 0.5) Very Low (0, 0, 0.25) Note that the input values, triangular fuzzy numbers fNO, fNS, and fND, used in Tables 1-3, respectively, have been taken because they are consistent with the "crisp" scores of the classic RPN calculation method and because they have been used and validated for case studies in real production environments.Although [33] uses trapezoidal functions to evaluate fNO, it is possible to find the equivalence in a triangular membership function, as shown in Mentes et al. [34], which is used and adapted to the equivalent "crisp" values 1-10 in [22].As for the values taken by different authors, they vary slightly; the values of Baghbani et al. [22] have been chosen for two reasons: first, because the triangular fuzzy numbers that were validated in a productive system contextualized in similar factories to the values that were considered in the case base of this work, and second, because they have been based on the data of Wang et al. [33], a main and contrasting source of the previously cited articles.
Using the L-R defuzzification methodology of Baghbani et al. [22], the weighted numbers can be obtained: µ W as µ T (W) over the weight factors µ WO , µ WS , and µ WD , according to five linguistic terms, W, as shown in Table 5, which expands on Table 4 above.Finally, once the defuzzified numbers of each risk factor µ O , µ S , and µ D and their relative importance through their weight factors µ WO , µ WS , and µ WD have been obtained, the risk priority number can be calculated using fuzzy logic, fRPN, as follows: The above formula is adapted from the formula proposed by Wang et al. [33].In summary, a new RPN calculation is obtained, in which the weaknesses of the classic method are resolved.This new calculation will be implemented in the source code of the software application of the assisted system.

Application and Results
In previous work, the objective of integrating case-based reasoning (CBR) and reliabilitycentered maintenance (RCM) methodologies was implemented in the Java programing language, the result of which is an independent computer application for the conductive RCM model, called driven-RCM.
This section has been divided into three phases, according to chronological order: the preparation of the case base used, the design and implementation of the CBR-RCM application, and its use to solve a new case raised, enabling the applicability of the conductive RCM method through the execution of the CBR-RCM application.

Case Base
The case base is made up of 35 cases, presented in Appendix A, through easy data dumping from the worksheets corresponding to 35 problems that actually occurred and were successfully resolved under the RCM methodology on a machine identified according to a machine tree in a hierarchy format (Section S, Installation I, Equipment E), to locate the area where the failure FF occurred for the function F. These cases pertain to the papermaking industry, where maintenance is essential, because it is a continuous process and a malfunction can have environmental consequences [35].

Design and Implementation of a Conductive RCM: Application
Upon the establishment of a structured attribute database, derived from the case base (see Appendix A), the initiation of the computer application unfolds, using the Java programing language within the Eclipse environment.However, the execution of the corresponding logical functioning flow of the CBR method transpires through queries.This procedural cycle encompasses two distinct stages.The initial stage is dedicated to the application of the CBR flow to the FMECA segment of the RCM method.This entails the recovery of failure modes within the case base, subsequently subjecting them to a comparative analysis with the novel problem being posed through consultation.The ensuing stage endeavors to reapply maintenance actions, entailing a comprehensive reassessment of parameters such as the risk priority number (RPN), maintenance task instruction, maintenance class, interval, and the assigned responsible workshop.
The focal point of this undertaking is the modification of the second stage, specifically in the RPN calculation.This involves the substitution of the conventional calculation with the fuzzy risk priority number (fRPN) methodology elucidated in Section 2. Therefore, with a concentrated emphasis on the second stage, denominated as driven-RCM within the CBR Cycle Review Activity, the code has been implemented to alter the risk priority number (RPN) by considering its occurrence, severity, and detection factors, employing the fuzzy RPN methodology.

Case Studies: Resolution of a New Failure Case Conducted by an Improved Assistance-Driven System
The deployment of the designed assistance system was initiated within a specific machine section, necessitating the application of an RCM design to enhance both reliability and maintainability.At this juncture, the use of the driven RCM becomes feasible through the purpose-designed and modified application that is delineated in the preceding section.This implementation affords distinct advantages, notably, the reduction in the time invested by users who are tasked with design responsibilities and the mitigation of human errors that are inherent in the handling of extensive case databases.
To assess the efficacy of the enhanced system, a distinct case, divergent from the one examined in our previous publication where the classic RPN calculation method was employed, has been evaluated.The input data for the new problem posed, as presented in the query window of Figure 2, describe a functional failure denoted as "failure" in the Section labeled "EW", without corresponding data entry for installation, concerning the Equipment labeled "BRAKES".The application's robustness is apparent, because it accommodates cases where input data, specifying the problem location, are absent.Users have the flexibility to describe only the problem without recording the severity/initiation/evaluation (S/I/E) data.
The three recovered cases, which are analogous to the presented problem, are retrieved in descending order of similarity.The first identified case with ID = 25 exhibits the highest similarity to the presented problem, followed by cases ID = 14 and ID = 15 as the second and third most similar instances within the case base, respectively.
Upon user selection of the case aligning the best with the requisites of the new scenario or problem, in this instance, ID = 25, as it stands as the most analogous to the presented problem, the review process proceeds.The start of the second stage of the employed RCM process ensues promptly, entailing a comprehensive review of the contextual information on the new problem.In this iteration, incorporating the novel RPN calculation method, the risk factors that are associated with occurrence, severity, and detection are systematically considered.The new risk priority number (RPN) is automatically computed using linguistic terms through fuzzy logic.
It is noteworthy that, in contrast to the preceding RPN calculation method, the information entered is no longer numerical on a scale of 1 to 10, but rather comprises linguistic expressions such as low, medium, and high.As depicted in the initial three pop-up windows within Figure 3, new dialog boxes emerge, soliciting information on the relative importance of each risk factor, facilitated through a drop-down list of terms.This innovation represents a departure from the previous calculation methodology, in which such evaluations were not undertaken.
In Figure 4, data on the values of the three risk factors of occurrence, severity, and detection are entered by choosing from a drop-down list the most appropriate term that defines each of them for the functional failure analyzed.In this way, the expert goes from trying to evaluate precisely and numerically to using a more natural language with human tolerance.As a result of the calculation, an information box appears with the new RPN value, calculated with the new implemented methodology, as shown in the last figure in Figure 4.
It should be noted that previously, the new method was validated with extreme and average values for the weights and risk factors, verifying RPN results in accordance with them.Finally, using similar input data for both classic/fuzzy weighted methodologies, RPN values are obtained, 300 vs. 336, respectively, resulting in a discrepancy of 1.78%, which indicates that the method has been well adjusted.
Continuing with the review process, in the same way as in our previous work, the source code implementation from now until the completion of the program has not been modified.Therefore, by reviewing the contextual information of the new problem, as shown in Figure 5, the new data are recorded: Interval (periodicity), Responsibility, and proposed maintenance task, respectively.ure in Figure 4.
It should be noted that previously, the new method was validated with extreme and average values for the weights and risk factors, verifying RPN results in accordance with them.Finally, using similar input data for both classic/fuzzy weighted methodologies, RPN values are obtained, 300 vs. 336, respectively, resulting in a discrepancy of 1.78%, which indicates that the method has been well adjusted.Continuing with the review process, in the same way as in our previous work, the source code implementation from now until the completion of the program has not been modified.Therefore, by reviewing the contextual information of the new problem, as shown in Figure 5, the new data are recorded: Interval (periodicity), Responsibility, and proposed maintenance task, respectively.The second revision stage comprises redefining the new maintenance policy or class  Continuing with the review process, in the same way as in our previous wo source code implementation from now until the completion of the program has n modified.Therefore, by reviewing the contextual information of the new prob shown in Figure 5, the new data are recorded: Interval (periodicity), Responsibili proposed maintenance task, respectively.The second revision stage comprises redefining the new maintenance policy following the RCM diagram, where the user has been guided through the question diagram, as shown in Figure 6.The maintenance policy is obtained as an output.work, the maintenance classification obtained is Maintenance by Operato The second revision stage comprises redefining the new maintenance policy or class following the RCM diagram, where the user has been guided through the questions in the diagram, as shown in Figure 6.The maintenance policy is obtained as an output.In this work, the maintenance classification obtained is Maintenance by Operator, thus completing the solution of the chosen case (see the last case in Figure 7a), which is split for better display.
Electronics 2024, 13, x FOR PEER REVIEW 12 of 18 completing the solution of the chosen case (see the last case in Figure 7a), which is split for better display.Finally, the retention activity is checked by verifying the persistence, i.e., that the new case is stored in the database RCM_EW.CSV file.The newly added case is also highlighted in Figure 7b, where it can be seen that case number 36, a consecutive number to the last existing case in the original cases base, contains all the values that were obtained in the solution process of the employed process according to Figures 4-7.Table 6 shows the attributes of Figure 7b.
In this new added case, Figure 7b, the values of the attributes identified in the S/I/E/FF columns have been automatically recovered as the input data from the problem posed, Query window Figure 2a, where F, FE, and FM are not shown for simplicity and are automatically recovered by the system and incorporated into the added case.In this new added case, the remaining values of the II/R/PT/fRPN/MC attributes have been recorded as a solution, which is finally adopted by the assisted system, because of the twostage process described above.The values of this resolved case are included in the case identified as IDC = E in Table 7.   Finally, the retention activity is checked by verifying the persistence, i.e., that the new case is stored in the database RCM_EW.CSV file.The newly added case is also highlighted in Figure 7b, where it can be seen that case number 36, a consecutive number to the last existing case in the original cases base, contains all the values that were obtained in the solution process of the employed process according to Figures 4-7.Table 6 shows the attributes of Figure 7b.
In this new added case, Figure 7b, the values of the attributes identified in the S/I/E/FF columns have been automatically recovered as the input data from the problem posed, Query window Figure 2a, where F, FE, and FM are not shown for simplicity and are automatically recovered by the system and incorporated into the added case.In this new added case, the remaining values of the II/R/PT/fRPN/MC attributes have been recorded as a solution, which is finally adopted by the assisted system, because of the twostage process described above.The values of this resolved case are included in the case identified as IDC = E in Table 7.  Finally, the retention activity is checked by verifying the persistence, i.e., that the new case is stored in the database RCM_EW.CSV file.The newly added case is also highlighted in Figure 7b, where it can be seen that case number 36, a consecutive number to the last existing case in the original cases base, contains all the values that were obtained in the solution process of the employed process according to Figures 4-7.Table 6 shows the attributes of Figure 7b.In this new added case, Figure 7b, the values of the attributes identified in the S/I/E/FF columns have been automatically recovered as the input data from the problem posed, Query window Figure 2a, where F, FE, and FM are not shown for simplicity and are automatically recovered by the system and incorporated into the added case.In this new added case, the remaining values of the II/R/PT/fRPN/MC attributes have been recorded as a solution, which is finally adopted by the assisted system, because of the two-stage process described above.The values of this resolved case are included in the case identified as IDC = E in Table 7.The rest of the cases studied have been collected in Table 7, with their attributes being presented in Table 6, as well as the values that can be selected in some of them.The previously solved problem is presented as IDC = E in Table 7.

Discussion
The novelty introduced in this work consists of successfully combining two methods that are used successfully in fuzzy logic to improve the calculation of the risk priority number (RPN), i.e., the fuzzy weighted geometric mean method developed by Wang et al. [29] and the defuzzification method used by Baghbani et al. [18] for RPN calculation.The advantage achieved is that it is not necessary to use tedious IF-THEN inference rules.In this work, the combination of both fuzzy logic methods, weighted L-R defuzzification, has been used to efficiently calculate the RPN in a more natural language and prioritizing the risk factors necessary to assess RPNs.
A set of five problems has been presented to be solved by the improved application of the assisted system.The same new case to be solved, case IDC = A from Table 7, has been presented again as in the previous work of Rodríguez-Padial et al. [5] on the new improved system, in such a way that when the second stage of the conductive RCM begins, the data inputs and the automatic calculation differ substantially, although this is not the case with the result, which, as has been verified, shows a discrepancy of 1.78%, which ensures a good fit of the new method used.This highlights the different implemented methodologies, i.e., classic RPN versus the new defuzzy-RPN methodology.The rest of the problems that were resolved by the improved application have been registered as IDC = B, C, D, and E. These new problems have been raised because they presented greater criticality in the RCM work groups that were conducted to create the case base.Therefore, B, C, and D, are three of the problems where the highest RPN were evaluated and have now been re-evaluated with the new RPN calculation methodology.
The values obtained by the new method are slightly lower than those obtained by the classic RPN method and vice versa, suggesting that the new method allows the RPN to be more homogenized.The application of the assistance-driven RCM system has been validated by taking comparable extreme and intermediate cases and obtaining the expected results.

Conclusions
The objective of this work was to improve the calculation of the risk priority number (RPN) in the assisted system already presented to design maintenance plans driven by CBR algorithms that are integrated into the RCM methodology.The classic RPN calculation method based on independently evaluating the three risk factors (occurrence, severity, and detection) is replaced by a weighted defuzzification method to calculate the same using linguistic terms.
The obtained result has substantially improved the application, modifying an extract of its source code in Java, so that the automatic RPN calculation routine has been improved, implementing the new weighted L-R defuzzification methodology.A final improvement achieved is the fact that the method for entering the information in this second stage, by using linguistic terms instead of specifying them through numerical values, in addition to comfort for the human expert to whom the system responds, represents a saving in devoted time.
Finally, five problems have been presented to be solved by the improved application of the assisted system, while one of the cases has made it possible to compare the discrepancy between the RPN according to the new and classic methods, posing the same problem as in our previous work.Once the validation of the new improved application has been verified, it is possible to measure how its precision is preserved.The remaining resolved cases have been chosen as those with the highest initial risk value, and in this work, they have been re-evaluated by the application using the new fRPN calculation method.The values obtained by the new method allow us to obtain a list of more homogeneous RPN values than those obtained by the classic method.
This work is limited to the few real cases that are applied; that is, the system that assisted with the new proposed RPN calculation method must be tested with more extensive case bases, validating and analyzing the differences between the classic and proposed methods.In extension, in future developments, it is suggested to perform a sensitivity analysis on the result obtained (fRPN) compared with the choices to be made regarding the risk factors.The pads must be adjusted to the height of the package and introduce a pressure between a minimum and a maximum to achieve adequate quality in the wrapped package.1st PRESS p1(min = 1_max = 2.5) bar.2nd PRESS p2(min = 0_max = 1.5) bar.

EW Resmas Pads
No adequacy of the minimum pressure according to the optimum operating value The pads must be adjusted to the height of the package and introduce a pressure between a minimum and a maximum to achieve adequate quality in the wrapped package.1st PRESS p1(min = 1_max = 2.5) bar.2nd PRESS p2(min = 0_max = 1.

Figure 1 .
Figure 1.Java development environment in the Eclipse integrated development environment (IDE) under the jCOLIBRI domain.

Figure 1 .
Figure 1.Java development environment in the Eclipse integrated development environment (IDE) under the jCOLIBRI domain.

Figure 2 .
Figure 2. Problem data: (a) input data; (b) output window with the three similar cases.

Figure 2 .
Figure 2. Problem data: (a) input data; (b) output window with the three similar cases.

Figure 3 .
Figure 3. Dialog boxes for the evaluation, in linguistic terms, of the relative importance of each risk factor: (a) occurrence probability; (b) severity probability; and (c) detection probability.

Figure 3 .
Figure 3. Dialog boxes for the evaluation, in linguistic terms, of the relative importance of each risk factor: (a) occurrence probability; (b) severity probability; and (c) detection probability.

Figure 4 .
Figure 4. Dialog boxes for the evaluation, in linguistic terms, of the relative importance of each risk factor: (a) occurrence degree; (b) severity degree; (c) detection degree; and (d) New RPN.

Figure 5 .
Figure 5. Continuation of the review process for required variables: (a) Interval; (b) Responsibility; (c) Task.

Figure 4 .
Figure 4. Dialog boxes for the evaluation, in linguistic terms, of the relative importance of each risk factor: (a) occurrence degree; (b) severity degree; (c) detection degree; and (d) New RPN.

Figure 4 .
Figure 4. Dialog boxes for the evaluation, in linguistic terms, of the relative importance of e factor: (a) occurrence degree; (b) severity degree; (c) detection degree; and (d) New RPN.

Figure 5 .
Figure 5. Continuation of the review process for required variables: (a) Interval; (b) Respon (c) Task.

Figure 5 .
Figure 5. Continuation of the review process for required variables: (a) Interval; (b) Responsibility; (c) Task.

Figure 6 .
Figure 6.Data review inputs for the new chosen case, through questions of operational context.Second stage, employed RCM applied to the maintenance policy.

Figure 6 .
Figure 6.Data review inputs for the new chosen case, through questions of operational context.Second stage, employed RCM applied to the maintenance policy.

Figure 6 .
Figure 6.Data review inputs for the new chosen case, through questions of operational context.Second stage, employed RCM applied to the maintenance policy.
Note that the acronyms used are as follows: OM = Operator Maintenance, RD = Redesign, CBM = Condition-Based Maintenance, TBM = Time-Based Maintenance, CM = Corrective Maintenance, PFF = Periodic Failure Finding for Maintenance Classification (MC), TM = Mechanical workshop, TE = Electrical workshop, PROD = Production operator, and MP = Preventive workshop for Responsibility (R).